Related papers: Regret and Belief Complexity Trade-off in Gaussian…

In the classical multi-armed bandit problem, instance-dependent algorithms attain improved performance on "easy" problems with a gap between the best and second-best arm. Are similar guarantees possible for contextual bandits? While…

Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven empirical success in applications, the cumulative regret upper bound of EI remains an open question. In this…

We consider the problem of optimizing an unknown (typically non-convex) function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS), based on noisy bandit feedback. We consider a novel variant of this problem in which the…

We present simple and efficient algorithms for the batched stochastic multi-armed bandit and batched stochastic linear bandit problems. We prove bounds for their expected regrets that improve over the best-known regret bounds for any number…

Much of the literature on optimal design of bandit algorithms is based on minimization of expected regret. It is well known that designs that are optimal over certain exponential families can achieve expected regret that grows…

We study the logistic bandit, in which rewards are binary with success probability $\exp(\beta a^\top \theta) / (1 + \exp(\beta a^\top \theta))$ and actions $a$ and coefficients $\theta$ are within the $d$-dimensional unit ball. While prior…

Many real-world optimization problems involve an expensive ground-truth oracle (e.g., human evaluation, physical experiments) and a cheap, low-fidelity prediction oracle (e.g., machine learning models, simulations). Meanwhile, abundant…

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement…

Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian…

We consider the adversarial multi-armed bandit problem under delayed feedback. We analyze variants of the Exp3 algorithm that tune their step-size using only information (about the losses and delays) available at the time of the decisions,…

Upper Confidence Bound (UCB) algorithms are a widely-used class of sequential algorithms for the $K$-armed bandit problem. Despite extensive research over the past decades aimed at understanding their asymptotic and (near) minimax…

This paper studies batched bandit learning problems for nondegenerate functions. We introduce an algorithm that solves the batched bandit problem for nondegenerate functions near-optimally. More specifically, we introduce an algorithm,…

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under…

We describe a novel algorithm for noisy global optimisation and continuum-armed bandits, with good convergence properties over any continuous reward function having finitely many polynomial maxima. Over such functions, our algorithm…

We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the…

I present the first algorithm for stochastic finite-armed bandits that simultaneously enjoys order-optimal problem-dependent regret and worst-case regret. Besides the theoretical results, the new algorithm is simple, efficient and…

Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei…

Multi-armed Bandit motivates methods with provable upper bounds on regret and also the counterpart lower bounds have been extensively studied in this context. Recently, Multi-agent Multi-armed Bandit has gained significant traction in…